On the inverse first-passage-time problem for a Wiener process

Abstract

The inverse first-passage problem for a Wiener process $(W_t{)}_{t\ge 0}$ seeks to determine a function $b:{\mathbb{R}}_{+}\to \mathbb{R}$ such that \[τ=\inf\{t>0| W_t\ge b(t)\}\] has a given law. In this paper two methods for approximating the unknown function $b$ are presented. The errors of the two methods are studied. A set of examples illustrates the methods. Possible applications are enlighted.

Published in at http://dx.doi.org/10.1214/08-AAP571 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)